The task of the Institute of Ship Technology and Ocean Engineering (ISMT) as part of the research cooperation is to develop mathematical models for roll damping. Which is referred to by the project title MAT-Roll.

The project aims at the development of a wide spectrum of practical methods for prediction of roll damping for modern ship hull forms, including „numerical towing tank“ CFD methods, simplified models for nonlinear seakeeping simulations and regression formulae.

The influence of the hull form, appendages and motion parameters is studied for a wide range of modern container vessels and ferries, using CFD methods.

Aside the two methods: experiment and simulation a mathematical model represents a third method to compute damping coefficients. The mathematical model can be defined by a differential equation whose solution describes the time dependent roll motion of a ship. The terms of the equation model the hydrodynamic effects acting on the ship hull and appendages. Some of these effects like uprighting moment or the rigid body dynamics of the hull can be easily computed. Other flow effects have to be determined. One possible method to obtain the unknown terms is to perform a polynomial expansion of the dependent variables and compute their coefficients by a least squares fit to the computed or measured time series.

The results obtained with the mathematical model only yield meaningful damping coefficients for the single measurement they were computed for. For other configurations they could only predict qualitative properties. To quantitatively determine the roll damping coefficients a hydrodynamic data base is set up with the results of test which input parameters has been varied and combined over a wide range of parameter. Based on these coefficients the regression model can predict roll behavior of new ship designs and allows to compute confidence intervals for the damping coefficients.